3/2 / 4/5 + 1/2 * 1/2 Simplify

3/2 / 4/5 + 1/2 * 1/2

You need parentheses.
Do you mean
(3/2 / 4/5 + 1/2) * 1/2 ?

or
3/2 / 4/5 + (1/2 * 1/2)?

the second one with out the parentheses around it

(3/2 )/(4/5)=(3*5)/(2*4)=15/8

(1/2)*(1/2)=1/4=2/8

(15/8)+(2/8)=17/8=(16+1)/8=(16/8)+(1/8)=
2 1/8

To simplify the given expression, we need to perform the operations of addition and multiplication in the correct order, according to the rules of operations (PEMDAS/BODMAS).

Let's break down the expression step by step:

Step 1: Division of fractions
To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction (i.e., flip the second fraction and multiply).

So, we have:
3/2 ÷ 4/5 + 1/2 * 1/2

Rewriting the expression using multiplication instead of division:
3/2 * 5/4 + 1/2 * 1/2

Step 2: Simplify each multiplication operation
To multiply fractions, multiply the numerators together and the denominators together.

For the first multiplication:
(3 * 5) / (2 * 4) + 1/2 * 1/2

Simplifying further:
15/8 + 1/2 * 1/2

For the second multiplication:
15/8 + (1 * 1) / (2 * 2)

Simplifying further:
15/8 + 1/4

Step 3: Finding a common denominator
To add fractions, we need to have the same denominator. In this case, the least common denominator (LCD) is 8.

Converting the first fraction to have a denominator of 8:
15/8 + (1/4 * 2/2)

Simplifying further:
15/8 + 2/8

Step 4: Adding the fractions
Add the numerators together and keep the common denominator.

(15 + 2) / 8

Simplifying the numerator:
17/8

Therefore, the simplified expression is 17/8.